Influence of spatially dependent properties on the performance of a thermoelectric heat pump

A study is presented of the performance of thermoelectric heat pumps with spatially dependent properties. The Seebeck coefficient, electrical resistivity and thermal conductivity are assumed to vary linearly with position. The performance criteria of interest include maximum no-load temperature difference, maximum coefficient of performance, maximum heat pumping capacity, coefficient of performance under conditions giving maximum heat pumping capacity and heat pumping capacity under conditions giving maximum coefficient of performance. Throughout the investigation it is assumed that the longitudinal surface of the thermoelement is insulated and that the fin conductances at the hot and cold junctions are infinite. The effect of spatial dependence of each property on the performance criterion is analyzed individually and then in physically appropriate combinations. It is shown that certain small linear variations in the Seebeck coefficient and the electrical resistivity act to increase all the performance criteria. However, small linear variations in the thermal conductivity decrease the performance criteria. In addition, it is shown that the spatial dependence of the thermal conductivity is not nearly as important as the dependence of the electrical resistivity and the Seebeck coefficient. Therefore, a net increase in the performance criteria should be possible through the use of controlled spatial property dependence.